Long Term Evolution (LTE) is the name given to a project within the Third Generation Partnership Project (3GPP) aiming to improve the Universal Mobile Telecommunications System (UMTS) mobile phone standard to cope with future requirements.
In Downlink (DL) transmissions, the LTE communications air interface, Evolved UMTS Terrestrial Radio Access (E-UTRA), uses Orthogonal frequency-division multiplexing (OFDM) with 15 kHz subcarrier spacing and up to 2048 subcarriers. The same carrier spacing and max bandwidth is applicable also in Uplink (UL) transmissions, although the communications air interface is based upon single-carrier frequency-division multiple access (SC-FDMA).
A user equipment in a radio communications network signals data to a radio base station for accessing the radio communications network or communicating within the radio communications network. The radio base station receives the data and processes the data according to a receiver chain, for example, an LTE UL Layer 1 (L1) receiver chain comprising the following steps:    1. Fast Fourier Transform (FFT) to extract users per antenna    2. Channel estimation per antenna and user    3. Combined maximal ratio combining (MRC) diversity technique, combining of antennas, and Equalization using the channel estimate from the channel estimation    4. Inverse Fast Fourier transform (IFFT)    5. Decoding
In LTE the channel estimation is based on reference symbols (RS) in a channel, these RS are sometimes called pilots. The channel can hence be estimated as a matched filter, that is, correlating the known structure of reference symbols in an ideal signal with the received reference symbols in real signal to detect the presence of the known structure in the real signal.
The equalization is based upon the channel estimation and the purpose of the equalization is to compensate for a frequency selective channel that might appear due to multi-path fading. Embodiments herein are related to the LTE UL receiver chain and in particular to the channel estimation procedure, but may also relate to similar systems performing channel estimation using discrete cosine transformation. The better the channel estimation becomes the better will the equalization work and the less errors will be introduced in the data flow.
Discrete Cosine Transform (DCT) can be used to improve the frequency channel response on RS. The DCT process transforms the estimated channel response, also referred to as estimated channel, to the DCT domain and truncates the estimated channel response. Since the channel response in DCT domain ends up in the first samples, also known as taps, whereas the noise is spread out, a truncation will significantly improve the signal to noise ratio.
The main benefit of using DCT is that it is efficient and simple to implement. A problem with DCT is however that the truncation in DCT domain causes spectral leakage in frequency domain. Applying truncation in DCT domain is similar to a rectangular window in time domain, which corresponds to convolution with a sinc function in frequency domain. This undesirable effect of truncation would cause more distortion to the channels with larger delay spread since large delay spread corresponds to a long tail in DCT domain and the channel's energy is sacrificed in the long tail by applying truncation. FIG. 1 shows an example of the difference between a real channel and an estimated channel by using DCT 11 with truncation and no truncation 10. The truncation is needed to improve the signal to noise ratio in the estimated channel without truncation 10. The channel in DCT domain is defined in the y-axis and the taps in the DCT domain are defined along the x-axis. The real channel 12 has four non-trivial taps, taps five and up are very close to zero, but the truncation only keep the first tap and set the other taps to zero, resulting in that channel data is removed by the truncation.